Question

For what value of "r" is the following statement an identity? ²-10-2/-4 = -6 + r/-4, provided that ≠ 4.

A) r = -8
B) r = 6
C) r = -6
D) There is no value of "r" that makes the statement an identity.

Answer 1

The value of 'r' that makes the given statement an identity is r = -4.

Step-by-step explanation:

To find the value of 'r' that makes the given statement an identity, we need to manipulate the equation and solve for 'r'.

We can start by simplifying both sides of the equation:

• On the left side, simplify the expression: (2 - 10 - 2) / (-4) = -10 / (-4) = 5/2
• On the right side, simplify the expression: (-6 + r) / (-4)

Since the equation is an identity, both sides must be equal, so we can set the simplified expressions equal to each other:

5/2 = (-6 + r) / (-4)

To solve for 'r', we can multiply both sides of the equation by -4:

5/2 * -4 = -6 + r

-10 = -6 + r

To isolate 'r', we can subtract -6 from both sides:

r = -10 - (-6)

r = -10 + 6

r = -4

Therefore, the value of 'r' that makes the given statement an identity is r = -4. Option D is the correct answer.